What is the index number for the base year itself, and why?

It is always 100 , because the base year's price is being compared with itself. An index number above 100 then means a price rise since the base year, and one below 100 means a fall.

What is the difference between the RPI and the CPI?

Both track the changing prices of everyday goods and services, but the CPI leaves out mortgage payments while the RPI includes them. The government uses the RPI to set student loan interest, and the CPI to set benefits and the state pension.

True or False? Gross domestic product is a type of index number.

False. GDP is the total value of all the goods and services a country produces in a period, measured in money rather than against a base year. If it falls for two or more quarters in a row, the economy is said to be in recession.

What makes a weighted index number different from an ordinary one?

It tracks several items at once, with each item given a weight reflecting how important it is. The weighted mean price then takes the place of the single price, so the index compares this year's weighted mean with the base year's.

What does a chain base index number compare a price with?

The price in the previous year, or the previous month or quarter, rather than a fixed base year. Each period is measured against the one immediately before it, so there is no single base year at all.

A crude rate is the number of times an event happens in a population in a given period, usually stated per 1000 people . It is most often used for births and deaths, but marriages and unemployment can be measured in the same way.

A question asks for a town's crude marriage rate instead of its crude birth rate. What has to change in the formula?

Only the top of the fraction changes, with 'number of births' replaced by 'number of marriages'. The multiplication by 1000 and the division by the total population stay exactly the same, which is why one formula covers deaths and unemployment as well.

Why might two towns with the same number of deaths have different crude death rates?

Because the crude death rate divides the number of deaths by the total population, so the same number of deaths gives a higher rate in the town with fewer people. Working per 1000 people rather than with raw totals is what makes two populations of different sizes comparable.

GCSEStatisticsAQAHigherFlashcardsProcessing, Representing & Analysing DataIndex Numbers & Rates of Change

Index Numbers & Rates of Change (AQA GCSE Statistics: Higher): Flashcards

Exam code: 8382

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FrontIndex Numbers
Complete the formula for an index number.
$index number = \frac{current price of item}{______} \times______$

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Cards in this collection (18)

Complete the formula for an index number.
$index number = \frac{current price of item}{______} \times______$
The completed formula is:
$index number = \frac{current price of item}{price in base year} \times 100$
What is the index number for the base year itself, and why?
It is always 100, because the base year's price is being compared with itself.
An index number above 100 then means a price rise since the base year, and one below 100 means a fall.
A pint of milk cost 36p in the base year and costs 66p now. What is the index number?
Divide the current price by the base year price and multiply by 100, giving $\frac{66}{36} \times 100 = 183.3$ to one decimal place.
No percentage sign is used with an index number, even though the calculation itself is a percentage one.
The index number for widgets in 2022 is 112.3, with 2020 as the base year. What is the percentage change since 2020?
Subtract 100 from the index number, giving $112.3 - 100 = 12.3$ as the answer.
So prices rose by 12.3% between 2020 and 2022, and a negative result would have meant a fall instead.
A thingummy cost £56.50 in the base year, and the index number is now 107.2. What does it cost now?
Divide the index number by 100 to get the multiplier 1.072, then multiply the base year price by it.
That gives $56.50 \times 1.072 = 60.568$ pounds, which rounds to £60.57 as money.
What is the difference between the RPI and the CPI?
Both track the changing prices of everyday goods and services, but the CPI leaves out mortgage payments while the RPI includes them.
The government uses the RPI to set student loan interest, and the CPI to set benefits and the state pension.
True or False?
Gross domestic product is a type of index number.
False.
GDP is the total value of all the goods and services a country produces in a period, measured in money rather than against a base year.
If it falls for two or more quarters in a row, the economy is said to be in recession.
What makes a weighted index number different from an ordinary one?
It tracks several items at once, with each item given a weight reflecting how important it is.
The weighted mean price then takes the place of the single price, so the index compares this year's weighted mean with the base year's.
The weighted mean price of Roger's pizzas was £16.25 in 2019 and £18.88 in 2023. What is the 2023 weighted index number, taking 2019 as base?
Divide the current weighted mean by the base year weighted mean and multiply by 100.
$\frac{18.88}{16.25} \times 100 = 116.2$
What does a chain base index number compare a price with?
The price in the previous year, or the previous month or quarter, rather than a fixed base year.
Each period is measured against the one immediately before it, so there is no single base year at all.
Gold cost £42.61 per gram in April 2020 and £44.17 in May. What is the chain base index number for April to May?
Divide the May price by the April price and multiply by 100, giving $\frac{44.17}{42.61} \times 100 = 103.7$ to one decimal place.
April acts as the base month here, so the price rose by 3.7 per cent over that month.
Define crude rate.
A crude rate is the number of times an event happens in a population in a given period, usually stated per 1000 people.
It is most often used for births and deaths, but marriages and unemployment can be measured in the same way.
A town has a population of 40 000 and there were 520 births last year. What is the crude birth rate?
The crude birth rate is 13 births per 1000 people.
Multiply the number of births by 1000 and then divide by the total population.
$\frac{520 \times 1000}{40000} = 13$
A question asks for a town's crude marriage rate instead of its crude birth rate. What has to change in the formula?
Only the top of the fraction changes, with 'number of births' replaced by 'number of marriages'.
The multiplication by 1000 and the division by the total population stay exactly the same, which is why one formula covers deaths and unemployment as well.
True or False?
A question can ask for a crude rate per 100 people instead of per 1000.
True.
The formula works in exactly the same way with $\times 100$ used in place of $\times 1000$ and everything else unchanged.
Only do this when the question actually tells you to, because a crude rate is per 1000 people unless you are told otherwise.
A town of 33 500 people had a crude birth rate of 11.4 births per 1000 people. How many births were there?
There were 382 births.
Multiply the crude birth rate by the total population and then divide by 1000.
$\frac{11.4 \times 33500}{1000} = 381.9$
A number of births has to be a whole number, so this rounds to 382.
A town recorded 615 deaths last year and its crude death rate was 12.3 deaths per 1000 people. What is the town's population?
The town's population is 50 000.
Multiply the number of deaths by 1000 and then divide by the crude death rate.
$\frac{615 \times 1000}{12.3} = 50000$
Why might two towns with the same number of deaths have different crude death rates?
Because the crude death rate divides the number of deaths by the total population, so the same number of deaths gives a higher rate in the town with fewer people.
Working per 1000 people rather than with raw totals is what makes two populations of different sizes comparable.

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